Your Mind and How to Use It

CHAPTER XXVII

Deductive Reasoning

We have seen in the preceding chapter that from particular facts we reason inductively to general principles or truths. We have also seen that one of the steps of inductive reasoning is the testing of the hypothesis by deductive reasoning. We shall now also see that the results of inductive reasoning are used as premises or bases for deductive reasoning. These two forms of reasoning are opposites and yet complementary to each other; they are in a sense independent and yet are interdependent. Brooks says: “The two methods of reasoning are the reverse of each other. One goes from particulars to generals; the other from generals to particulars. One is a process of analysis; the other is a process of synthesis. One rises from facts to laws; the other descends from laws to facts. Each is independent of the other, and each is a valid and essential method of inference.”

Halleck well expresses the spirit of deductive reasoning as follows: “After induction has classified certain phenomena and thus given us a major premise, we may proceed deductively to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made premise. Deduction takes that as a fact, making no inquiry regarding its truth. Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed.”

Deductive reasoning proceeds from general principles to particular facts. It is a descending process, analytical in its nature. It rests upon the fundamental axiomatic basis that “_whatever is true of the whole is true of its parts_,” or “_whatever is true of the universal is true of the particulars_.”

The process of deductive reasoning may be stated briefly as follows: (1) A general principle of a class is stated as a _major premise_; (2) a particular thing is stated as belonging to that general class, this statement being the _minor premise_; therefore (3) the general class principle is held to apply to the particular thing, this last statement being the _conclusion_. (_A “premise” is “a proposition assumed to be true.”_)

I. (_Major premise_)–Rattlesnakes frequently bite when enraged, and
their bite is poisonous.

II. (_Minor premise_)–This snake before me is a rattlesnake;
therefore

III. (_Conclusion_)–This snake before me may bite when enraged, and
its bite will be poisonous.

The average person may be inclined to object that he is not conscious of going through this complicated process when he reasons about sparrows or rattlesnakes. But he _does_, nevertheless. He is not conscious of the steps, because mental habit has accustomed him to the process, and it is performed more or less automatically. But these three steps manifest in all processes of deductive reasoning, even the simplest. The average person is like the character in the French play who was surprised to learn that he had “been talking prose for forty years without knowing it.” Jevons says that the majority of persons are equally surprised when they find out that they have been using logical forms, more or less correctly, without having realized it. He says: “A large number even of educated persons have no clear idea of what logic is. Yet, in a certain way, every one must have been a logician since he began to speak.”

There are many technical rules and principles of logic which we cannot attempt to consider here. There are, however, a few elementary principles of correct reasoning which should have a place here. What is known as a “syllogism” is the expression in words of the various parts of the complete process of reasoning or argument. Whately defines it as follows: “A syllogism is an argument expressed in strict logical form so that its conclusiveness is manifest from the structure of the expression alone, without any regard to the meaning of the term.” In short, _if_ the two premises are accepted as correct, it follows that there can be only one true logical conclusion resulting therefrom. In abstract or theoretical reasoning the word “_if_” is assumed to precede each of the two premises, the “therefore” before the conclusion resulting from the “if,” of course. The following are the general rules governing the syllogism:–

I. Every syllogism must consist of three, and no more than three, propositions, namely (1) the major premise, (2) the minor premise, and (3) the conclusion.

II. The conclusion must naturally follow from the premises, otherwise the syllogism is invalid and constitutes a fallacy or sophism.

III. One premise, at least, must be affirmative.

IV. If one premise is negative, the conclusion must be negative.

V. One premise, at least, must be universal or general.

VI. If one premise is particular, the conclusion also must be particular.

The last two rules (V. and VI.) contain the essential principles of all the rules regarding syllogisms, and any syllogism which breaks them will be found also to break other rules, some of which are not stated here for the reason that they are too technical. These two rules may be tested by constructing syllogisms in violation of their principles. The reason for them is as follows: (Rule V.) Because “from two particular premises no conclusion can be drawn,” as, for instance: (1) Some men are mortal; (2) John is a man. We cannot reason from this either that John _is_ or _is not_ mortal. The major premise should read “_all_ men.” (Rule VI.) Because “a universal conclusion can be drawn only from two universal premises,” an example being needless here, as the conclusion is so obvious.

CULTIVATION OF REASONING FACULTIES.

There is no royal road to the cultivation of the reasoning faculties. There is but the old familiar rule: Practice, exercise, use. Nevertheless there are certain studies which tend to develop the faculties in question. The study of arithmetic, especially mental arithmetic, tends to develop correct habits of reasoning from one truth to another–from cause to effect. Better still is the study of geometry; and best of all, of course, is the study of logic and the practice of working out its problems and examples. The study of philosophy and psychology also is useful in this way. Many lawyers and teachers have drilled themselves in geometry solely for the purpose of developing their logical reasoning powers.

Brooks says: “So valuable is geometry as a discipline that many lawyers and others review their geometry every year in order to keep the mind drilled to logical habits of thinking. * * * The study of logic will aid in the development of the power of deductive reasoning. It does this, first, by showing the method by which we reason. To know how we reason, to see the laws which govern the reasoning process, to analyze the syllogism and see its conformity to the laws of thought, is not only an exercise of reasoning but gives that knowledge of the process that will be both a stimulus and a guide to thought. No one can trace the principles and processes of thought without receiving thereby an impetus to thought. In the second place, the study of logic is probably even more valuable because it gives practice in deductive thinking. This, perhaps, is its principal value, since the mind reasons instinctively without knowing how it reasons. One can think without the knowledge of the science of thinking just as one can use language correctly without a knowledge of grammar; yet as the study of grammar improves one’s speech, so the study of logic can but improve one’s thought.”

In the opinion of the writer hereof, one of the best though simple methods of cultivating the faculties of reasoning is to acquaint one’s self thoroughly with the more common _fallacies_ or forms of false reasoning–so thoroughly that not only is the false reasoning detected at once but also the _reason_ of its falsity is readily understood. To understand the wrong ways of reasoning is to be on guard against them. By guarding against them we tend to eliminate them from our thought processes. If we eliminate the false we have the true left in its place. Therefore we recommend the weeding of the logical garden of the common fallacies, to the end that the flowers of pure reason may flourish in their stead. Accordingly, we think it well to call your attention in the next chapter to the more common fallacies, and the reason of their falsity.